All four answers are grammatically correct, and could theoretically work. The best answer is A, the possessive form of “each other”. This means person X asks about person Y’s work, and person Y asks about person X’s work. As an exercise, this is, in my opinion, rather useless. Learn the most useful grammar, vocabulary, etc., first. Now if this is test preparation, and you’re just looking to beat one test, it may be another story.

Hi friend it's singular each other's work. It's an expression, you can't change it. 's is for possession ,in singular we say: Ex:it's our friend's car. In plural: Ex:The cars are for ethenic groups.They're ethenic groups' cars.